Mathisson-Papapetrou equations in metric and gauge theories of gravity in a Lagrangian formulation

Abstract

We present a simple method to derive the semiclassical equations of motion for a spinning particle in a gravitational field. We investigate the cases of classical, rotating particles (pole-dipole particles), as well as particles with intrinsic spin. We show that, starting with a simple Lagrangian, one can derive equations for the spin evolution and momentum propagation in the framework of metric theories of gravity and in theories based on a Riemann-Cartan geometry (Poincare gauge theory), without explicitly referring to matter current densities (spin and energy-momentum). Our results agree with those derived from the multipole expansion of the current densities by the conventional Papapetrou method and from the WKB analysis for elementary particles.

28 pages

References in corpus (2)

• Constrains on non-Newtonian gravity from the experiment on neutron quantum states in the Earth's gravitational field
• Autoparallel orbits in Kerr Brans-Dicke spacetimes

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